Ah... you were thinking of 'daisy-chaining' splitters. A preferred system design in applications such as mid-sized and larger apartments uses a high output distribution amplifier together with feed-through taps. That's the subject of the article I linked to.
Feed-through taps are somewhat like splitters but provide high isolation between the trunk ports and the drop port(s). They have the advantage of little loss between the two trunk ports and no need to terminate the drop port(s). The down-side is that you need to engineer the system to provide reasonably equal signal levels into the distribution amplifier. Here is an example of a programmable/agile filter/amplifier intended for use in a commercial quality MATV system:
http://www.dastechnology.co.uk/docs/...28SAF7U%29.pdf A calibrated signal level meter is needed to adjust the system.
In a three story twelve unit apartment, it may be less expensive and easier to maintain if you use a passive 3-way splitter at the antenna. Then run a 'trunk' to each floor. If needed, on each floor, a CM-3414 4-port distribution amplifier would provide an output to each unit. There would be plenty of signal power to drive a passive 4-way splitter in each unit.